The authors of CSRNet [1]}, as mentioned above, have been the first ones to demonstrate that multi-column networks suffer from many significant drawbacks. But furthermore, they also introduced a novel single-column cnn-based approach that can perform accurate density estimation and that represents a new milestone for the counting task. In particular, they presented CSRNet - Congested Scene Recognition Network, which can understand highly congested scenes and perform accurate count estimation as well as produce high-quality density maps. In particular, the network is composed of two major components. Following other previous work, like [2]}, the authors use a modified version of the well-known VGG-16 network [3]} as the front-end for 2D feature extraction because of its strong transfer learning ability, carving the first 13 layers and adding a \(1\times 1\)  convolutional layer as the output layer. The output size of this front-end network is \(1/8\)  of the original input size. The authors argue that continuing to stack more convolutional layers and pooling layers (i.e., the basic components in the VGG-16 network) would have led to an output size further shrunken, with the consequence of low-quality density maps. On the other hand, inspired by [4]}, [5]}, [6]}, they proposed a back-end consisting of dilated kernels. The basic concept of dilated convolutions is to deliver larger reception fields replacing the pooling operations, extracting deeper information of saliency, and maintaining the output resolution. Formally, a 2-D dilated convolution can be defined as follow:
\(y(m, n) = \sum _{i=1}^{M} \sum _{j=1}^{N} x(m + r \times i,n + r \times j) w(i,j),\) 
